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HSC 2013 MX2 Marathon (archive) (2 Viewers)

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seanieg89

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Re: HSC 2013 4U Marathon

Got up to iii, faced a problem:



Am I missing something here?


(Also I am very close to solving the last question)
Why does imply that ?
 

seanieg89

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Re: HSC 2013 4U Marathon

True that, well is this a good justification?













Not sure if my reasoning is correct
Why is < tw , z > smaller than < z , z >?

Seems correct if you can justify this step :).
 

Sy123

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Re: HSC 2013 4U Marathon

Why is < tw , z > smaller than < z , z >?

Seems correct if you can justify this step :).
I think i figured out how to justify it hehe (its pretty simple, not sure why I couldn't see it earlier)





Now for the last question (Ill post a full solution once I (if I) answer it))
 

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Re: HSC 2013 4U Marathon





Difficulty: Moderate

It would also be great if people could rate the difficulty of their own question as I have just done.


 
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Examine

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Re: HSC 2013 4U Marathon

Nice.



bit harder.
Challenge: Extend this question further so we have expressions like arctan(...) + arctan(...) = pi/4, where (...) are functions in terms of x.
 

Sy123

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Re: HSC 2013 4U Marathon

Challenge: Extend this question further so we have expressions like arctan(...) + arctan(...) = pi/4, where (...) are functions in terms of x.
Nice work on the above question, but for this, we can arrive at two variables:



Apply the tangent function to everything:



Simplify and we get:



Hence I think it can only be expressed as two variables not just in terms of single function x.

===========================



An easier one:





(I edited it, sorry for the inconvenience)
 
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seanieg89

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Re: HSC 2013 4U Marathon

I think i figured out how to justify it hehe (its pretty simple, not sure why I couldn't see it earlier)





Now for the last question (Ill post a full solution once I (if I) answer it))
You are close to the right idea, the key is that < z-tw, z-tw > is non-negative. Expand this expression out and you will get what you want :).

The final part of the question should be easier once you interpret it correctly.
 

seanieg89

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Re: HSC 2013 4U Marathon

Don't be mean....4U questions only here. No Polylogarithms please.
Evaluating the definite integral is well within the scope of MX2, the substitution



kills it.
 
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